Can one be addicted by taking the drugs only once?

I often drive past a billboard that says so. Does that make it true?

It certainly depends .....the majority of people do not get depended after their first alcoholic drinks, some do.
Some after their first cigarette others would never try to smoke again.

You say "the drugs," which drugs would those be?

If you only take a drug once, how would you know that you were addicted?

It happened to Barney Gumble.

I guess that might be when you are unable to refrain from dose #2.

Some drugs like Heroin can be said to do so, but it really depends what you mean by addiction. A substantial portion of addiction is mental, and it is certainly true that you can develop addicting-level cravings for a variety of things after trying them once.

As to the physical component many drugs have a "coming down" phase that is unpleasant and a return to reality that may not be as pleasant (both mentally and physically) as the effect of the drug.

I was totally hooked after my first hit of adrenalin.

I don't think so that one can be addicted even after taking it foe once. However it can be possible as well.